已知x+y=9,xy=10,求x^2+y^2,x^3+y^3,x^4+y^4的值。

(x+y)²=81
x²+y²+2xy=81
所以x²+y²=81-2xy=61

x³+y³
=(x+y)(x²-xy+y²)
=9×(61-10)
=459

(x²+y²)²=61²
x^4+2x²y²+y^4=3721
所以x^4+y^4=3721-2(xy)²=3521

x^2+y^2=(x+y)²-2xy=9²-2*10=61
x^3+y^3=(x+y)(x²-xy+y²)
=(x+y)[(x²+y²)-xy]
=9*(61-10)
=459
x^4+y^4
=(x^4+2x²y²+y^4)-2x²y²
=(x²+y²)²-2(xy)²
=61²-2*10²
=3721-200
=3521

x²+y²=(x+y)²-2xy=10²-2*9=100-18=82
x^3+y^3=(x+y)(x²-xy+y²)=(x+y)[(x+y)²-3xy]=9*(9²-3*10)=9*(81-30)=9*49=441
x^4+y^4=x^4+2x²y²+y^4-2x²y²=(x²+y²)²-2x²y²=82²-2*10²=6524

望采纳~谢谢

(x+y)^2=x^2+y^2+2xy=81

x^2+y^2=81-2xy=61

x^3+y^3=(x+y)(x^2+y^2-xy)=9*(61-10)=459

x^4+y^4=(x^2+y^2)^2-2(xy)^2=61^2-2*100=3521

1、x²＋y²=(x＋y)²－2xy=9²－20=61
2、x³＋y³=(x＋y)(x²－xy＋y²)=9×(61－10)=459
3、x^4＋y^4=(x²＋y²)²－2(xy)²=61²－200=3521

x²+y²=(x+y)²-2xy=81-20=61
x ³+y³=(x+y)(x²-xy+y²)=9(61-10)=459
x^4+y^4=(x²+y²)²-2x²y²=61²-200=3721-200=3521